# How to select a distribution for parameters?

I’m a new user for effective quadratures, and I’m trying to think about how to describe my parameters for a sensitivity analysis. This discourse has a great example case (Sensitivity Analysis with Effective Quadratures) , but I notice that the inputs are all uniform distributions.

Is there any guidance on how to select an appropriate distribution?

I’m planning to perform model runs (the COAWST model) where I have a guess as to “best” model parameter values, but I want to know the impact that the parameter values have on model outputs. For one parameter, I think a reasonable range is [best guess/ 2 to best guess * 2], but it may be that best guess/ 2.1 is also fine. This makes me think that a uniform distribution may not be appropriate, and perhaps gaussian is better? If the answer is “try it a few different ways and look at the impact”, what I should be looking for?

Thank you for the guidance! Feel free to point me towards other answers - I’ve found this discussion which seemed pertinent, but not complete:

Hi @rmallen86, welcome to discourse!

1. If you have data, you can use the data-driven approach, using the `data` distribution option, as per this link.

2. You can assume a uniform distribution for now, perhaps even with `endpoints`, and later try to use the `Poly` instance you generate but with different input distributions. In other words, you would effectively create a surrogate assuming a uniform distribution, and use that surrogate under a different input distribution. This should yield similar results assuming the distributions aren’t wildly distinct.

In terms of what you should be looking for, I would suggest you look at the mean and variance of the `Poly` instance – to query how they vary under different input distributions.

I would also try to run a couple of test cases within the input domain selected, and query if the `Poly`'s prediction at the test inputs aligns closely with the output of the COAWST model.

Hope this helps.

Thanks @psesh , I"ll give this a shot. May take me a little while, but I’ll post back here if I find more questions, or if it goes well and I want to share some results!

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